What is expand (Δx+x)^3 ?

The solution to expand (Δx+x)^3 is Δ^3x^3+3Δ^2x^3+3Δx^3+x^3

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expand (Δx+x)^3

expand

(Δ x + x)^{3}

Δ^{3} x^{3} + 3 Δ^{2} x^{3} + 3Δ x^{3} + x^{3}

Solution steps

(Δ x + x)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = Δ x, b = x

= (Δ x)^{3} + 3 (Δ x)^{2} x + 3Δ x x^{2} + x^{3}

Simplify

(Δ x)^{3} + 3 (Δ x)^{2} x + 3Δ x x^{2} + x^{3} : Δ^{3} x^{3} + 3 Δ^{2} x^{3} + 3Δ x^{3} + x^{3}

= Δ^{3} x^{3} + 3 Δ^{2} x^{3} + 3Δ x^{3} + x^{3}

\frac{3 x - 1}{( x ^{2} - 9 ) ( x ^{2} - 1 )}

(3 x^{2} + x + 3 \circ x + 4) (- 1)

- 10 (52 - 8)

(cos (\frac{2 π}{9}) - cos (x))^{2} + (sin (\frac{2 π}{9}) - sin (x))^{2}

(y - \frac{3}{2} x) (y - \frac{1}{2} x) (y - \frac{2}{15} x)

What is expand (Δx+x)^3 ?
The solution to expand (Δx+x)^3 is Δ^3x^3+3Δ^2x^3+3Δx^3+x^3